The Biot-Allard poro-elasticity system: equivalent forms and well-posedness

Abstract

We consider the fully dynamic Biot-Allard model, which includes memory effects. Convolution integrals in time model the history of the porous medium. We use a series representation of the dynamic permeability in the frequency domain to rewrite the equations in a coupled system without convolution integrals, suitable for the design of efficient numerical approximation schemes. The main result is the well-posedness of the system, proved by the abstract theory of R. Picard for evolutionary problems.